Radar Error Research Articles

Inverse Synthetic Aperture Radar Sparse Imaging Exploiting the Group Dictionary Learning

Sparse imaging relies on sparse representations of the target scenes to be imaged. Predefined dictionaries have long been used to transform radar target scenes into sparse domains, but the performance is limited by the artificially designed or existing transforms, e.g., Fourier transform and wavelet transform, which are not optimal for the target scenes to be sparsified. The dictionary learning (DL) technique has been exploited to obtain sparse transforms optimized jointly with the radar imaging problem. Nevertheless, the DL technique is usually implemented in a manner of patch processing, which ignores the relationship between patches, leading to the omission of some feature information during the learning of the sparse transforms. To capture the feature information of the target scenes more accurately, we adopt image patch group (IPG) instead of patch in DL. The IPG is constructed by the patches with similar structures. DL is performed with respect to each IPG, which is termed as group dictionary learning (GDL). The group oriented sparse representation (GOSR) and target image reconstruction are then jointly optimized by solving a l1 norm minimization problem exploiting GOSR, during which a generalized Gaussian distribution hypothesis of radar image reconstruction error is introduced to make the imaging problem tractable. The imaging results using the real ISAR data show that the GDL-based imaging method outperforms the original DL-based imaging method in both imaging quality and computational speed.

On the errors involved in ice-thickness estimates I: ground-penetrating radar measurement errors – ERRATUM

On the errors involved in ice-thickness estimates I: ground-penetrating radar measurement errors – ERRATUM

Dependence between the accuracy of target designation to an onboard missile radar station and errors related to determination of the target and missile coordinates by a ground radar system

This article investigates the dependence between the accuracy of target designation issued by a ground radar system to an onboard radar station based on the measured target and missile coordinates and on the relative missile position (relative to the radar and the target). Simulation and calculation methods are proposed for estimating the accuracy of target designation in terms of the observation angle and the range and speed of the target taking into account both the errors in measuring the target and missile coordinates by a ground radar system and the relative position of the missile. The influence of the errors in measuring the target and missile coordinates and the relative position of the missile on the target designation accuracy is investigated. The problem of tracing the optimal trajectory of missile guidance to the target is formulated taking into account the errors of target designation to an onboard radar station and other factors.

Correcting method of slant-range error for the TH-2 satellites

ABSTRACT A method of correcting the slant-range error of the space-borne interferometric synthetic aperture radar (InSAR) system aboard the TH-2 satellites is proposed. First, we calculate the tropospheric-delay using the third-order fractional mapping-function method, and we calculate the ionospheric-delay using the ray-tracing method. The calculations show that the atmospheric-delays for the TH-2 ranges from 2.23 m to 3.08 m in four areas. Next, From the channel-delay at corner-reflectors (CRs), we determine the average channel-delay to be 4.02 m from data-processing results for 22 scenes. Finally, we use the field data obtained by TH-2 to evaluate the effect of the slant-range correction. After correcting for the slant-range error, the accuracy of image-point coordinate prediction in the range direction is improved from about 7 pixels to less than one pixel. The ground-point positioning accuracy in elevation is also improved by about 4.65 m, and the plane accuracy approaches the elevation accuracy. The method proposed in this paper has been used to correct the slant-range error of TH-2, and the expected results have been achieved.

Radar Accuracy Modeling and Its Application to Object Vehicle Tracking

For advanced active safety systems and autonomous vehicles, it is essential to predict target vehicle behaviors. Radar is a reliable vehicular sensor, but it has a degree of measurement uncertainty because of its operational mechanism and wandering reflection point. To deal with this problem, this paper proposes a radar accuracy model for object vehicle tracking to reduce the tracking error of the radar system. First, we divide the area uniformly and identify the surrounding vehicles using information, including relative position and relative velocity.We then analyze the error characteristics of each uniformly divided area. Next, we develop an occupancy zone-based Kalman filter for each area based on the error characteristics. We solve the problem that one cannot assign an exact zone for the object vehicle due to radar error by using interacting multiple model (IMM) filter. The performance of the proposed method is validated via experiments using radar and ground truth data.

Influence of motion characteristics of dual stealth aircraft on monopulse radar performance

In view of the difficulties to effectively evaluate the influence of penetration of dual stealth aircraft formation on monopulse radar angle tracking error under different flight speeds, the dynamic track model of the dual stealth aircraft under different navigation speeds is established for the first time, and the acquisition method of the dynamic Radar cross section of the dual stealth aircraft formation under different navigation speeds is proposed; the dynamic signal-to-noise ratio of the dual stealth aircraft under different navigation speeds is used as a reference and the model of single pulse radar angle tracking error is established. This paper analyzes the influence of the formation motion characteristics of dual stealth aircraft on the angle tracking error performance of monopulse radar. It is the first time to conclude that the acceleration of the navigation speed of dual stealth aircraft will increase the angle tracking error of monopulse radar when there is no interference.

Two-stage autofocus algorithm with filled function for synthetic aperture radar

Entropy-based parametric autofocus is commonly applied to correct the residual azimuth phase error (APE) that arises from the residual motion errors (RME) in synthetic aperture radar. However, the image’s entropy trends to a convex function only when a great number of range bins are selected according to the law of large numbers, which means that the average residual APE is finally obtained via this method for the space-variant characteristics of RME. A two-stage parametric autofocus algorithm is carried out to derive the exact residual APE with several range bins selected for iteration. To this end, a new objective function in the first stage is designed to reduce the number of local solutions and protect targets from energy leaking. In the second stage, the filled function is imported to jump out of the current solution to a more optimal one until no other optimal solution exists. In the final part, both simulated and real data experiments validate the performance of the proposed method.

Cramer-Rao Bounds of Localization Estimation for Integrated Radar and Communication System

Instead of only considering the radar estimation error in the traditional radar system (TRS), for the integrated radar and communication system (IRCS), we investigate the Cramer-Rao bound (CRB) of the localization estimation, which is influenced by both radar estimation error and communication transmission error. The functions of radar and communication are operated simultaneously by embedding the communication symbols into the multicarrier radar waveforms. Firstly, we derive the CRB of time/direction of arrival (TOA/DOA) estimation. To minimize the estimation error, we maximize the signal-to-interference-plus-noise ratio (SINR) of radar by iteratively optimizing the radar transmit and receive beamformers (with the constraint of available transmit power). Then, the CRB of localization estimation is derived using hybrid TOA/DOA measurement. The local CRBs from different IRCSs are fused according to the linear fusion rule at the fusion center (FC). Finally, numerical results demonstrate that the additional estimation errors for the IRCS are mainly determined by the channel conditions of communication and available transmit power; the estimation accuracy for both IRCS and TRS can be improved through the iterative transmit and receive beamforming (ITRB) technique.

An Optimizing Method of OFDM Radar Communication and Jamming Shared Waveform Based on Improved Greedy Algorithm

Orthogonal frequency division multiplexing (OFDM) has been widely used as radar, communication, and jamming shared waveform. To improve the power utilization and efficiency of radar, communication, and jamming integrated system, we propose an adaptive OFDM shared waveform design method. Considering the problem of jamming path propagation loss and sensitivity of frequency response error of radar and communication channels, we propose a robust OFDM shared waveform design method. Firstly, the suppressed jamming entropy model, the detection probability (Pd) of the stationary point target model, the data information rate (DIR) model with a given bit error rate (BER) are formulated. With the constraints on total power and BER, the adaptive and the robust OFDM optimization problems are formulated. Then we derive the Karush-Kuhn-Tucker (KKT) conditions of the two optimization problems and an improved greedy algorithm is proposed to solve the optimization problems, and the optimal power and bit allocation schemes for the two problems are obtained. Finally, we present several numerical results to demonstrate the effectiveness of the proposed method.

An Algorithm for Estimating and Correcting Decorrelation Phase From InSAR Data Using Closure Phase Triplets

We propose a novel method for quantifying and correcting phase errors in interferometric synthetic aperture radar (InSAR) data associated with signal decorrelation. This proposed method relates the observed phase nonclosure (referred to as the closure phase) of triplet combinations of any three individual SAR scenes to the decorrelative phase signal in individual interferograms (pairs of SAR scenes). A singular value decomposition (SVD) method is applied to solve the minimum-norm least-squares best fitting estimate of the decorrelation phase for any arbitrary collection of SAR images. This decorrelative phase is then removed from individual interferograms; these corrected interferograms can then be used with existing InSAR time-series analysis algorithms. We demonstrate this method on the Advanced Land Observation Satellite Phased Array type L-band Synthetic Aperture Radar (ALOS PALSAR) scenes of a groundwater pumping subsidence feature in the Central Valley of California and briefly discuss potential future applications of this algorithm to study a variety of environmental and surface physical processes that contribute to InSAR signal decorrelation.

Approach of system error registration for two‐station coast radars for sea surface monitoring

In the multi-radar tracking system, multi-radar data fusion technology can improve the detection and tracking capabilities of radar. Besides, the spatial registration processing of radar data can effectively calibrate the radar system error and improve the fusion accuracy. In this study, the system error registration for two-station coast radars based on non-cooperative targets is implemented by using the exact maximum likelihood spatial registration algorithm (EML). On the basis of the EML algorithm, this study proposes a selection method for the corresponding targets. The selection method that facilitates the application of the EML algorithm can automatically complete the clipping, alignment and registration of the track information. For the defect that the EML algorithm is easy to fall into the local minimum in the iterative processing, the data inspection method based on the minimum root mean square test is proposed in this study, which can further improve the exactitude of the system error estimation. Compared with direct fusion, the plot fusion accuracy of the two-station coast radars is significantly improved after the spatial registration of the EML algorithm.

Error Mitigation Algorithm Based on Bidirectional Fitting Method for Collision Avoidance of Unmanned Surface Vehicle

Abstract Radars and sensors are essential devices for an Unmanned Surface Vehicle (USV) to detect obstacles. Their precision has improved significantly in recent years with relatively accurate capability to locate obstacles. However, small detection errors in the estimation and prediction of trajectories of obstacles may cause serious problems in accuracy, thereby damaging the judgment of USV and affecting the effectiveness of collision avoidance. In this study, the effect of radar errors on the prediction accuracy of obstacle position is studied on the basis of the autoregressive prediction model. The cause of radar error is also analyzed. Subsequently, a bidirectional adaptive filtering algorithm based on polynomial fitting and particle swarm optimization is proposed to eliminate the observed errors in vertical and abscissa coordinates. Then, simulations of obstacle tracking and prediction are carried out, and the results show the validity of the algorithm. Finally, the method is used to simulate the collision avoidance of USV, and the results show the validity and reliability of the algorithm.

Centralized Adaptive CFAR Detection With Registration Errors in Multistatic Radar

The problem of centralized adaptive constant false alarm rate (CFAR) detection with registration errors in multistatic radar is considered. When the observation data from different radar sites are not properly aligned after transformed into a common coordinate system, registration errors occur. This can severely degrade the target detection performance and positioning accuracy of multistatic radar. In this paper, we focus on the design of adaptive detectors that are applicable for centralized target detection with registration errors in multistatic radar. A maximum likelihood estimation-based generalized likelihood ratio test detector and a maximum a posteriori estimation-based generalized likelihood ratio test detector are developed. Both detectors possess the CFAR property with regard to the unknown statistics of the background noise. Accordingly, the performance of the two proposed detectors are analyzed.

A Channel Phase Error Correction Method Based on Joint Quality Function of GF-3 SAR Dual-Channel Images.

Multichannel SAR is an effective approach to solving the contradiction between high azimuth resolution and wide swath. The goal of this paper is to obtain a new and effective method for estimating and compensating the interchannel phase error of the Chinese GF-3 Synthetic aperture radar (SAR). A channel phase error correction method based on the optimal value of the image domain quality function is proposed. In this method, the phase error is initially compensated using the correlation function method. In the fine correction of dual-channel phase error, a heuristic search algorithm is used to estimate the residual phase by searching the extremum of the quality function. After phase compensation in the image domain, the azimuth ambiguities caused by the remaining phase are eliminated. The proposed image domain processing method provides a new idea for channel phase error correction. The measured data of high-resolution GF-3 dual-channel ultrafine imaging mode verifies the validity of this method.

우주감시레이다에 대한 지구 대기권 영향 분석 연구

In this study, both the altitude error due to the refraction and the range error due to the delay in the ionosphere with respect to the frequency are extracted according to the radar elevation to analyze the effect of atmosphere on the space surveillance radar. To achieve this, the radio refractivity profile is modeled using the measured data from domestic weather stations. Then, the altitude-error due to the refraction is extracted using the ray tracing method, and the range error in the ionosphere is extracted according to the frequency. Further, considerations for radar design with respect to the radar error characteristics are discussed based on the abroad space surveillance radar and proposed domestic space surveillance radar. This analysis of the error characteristics is expected to be utilized for the determination of radar location, range of steering, and frequency in the space surveillance radar design.

METHOD FOR ESTIMATING ERRORS IN MEASURING INSTRUMENTS BY THE SPACE CATALOGUE ORBITS

Improvement of orbits precision is one of the most important tasks of space surveillance catalogue maintenance. The solution of this problem is directly related to an adequate consideration of the errors of the coordinate information from the measuring instruments. The article consideresd a new method for estimating the precision of measuring instruments on the catalog orbits. To carry out such analysis, in PJSC «VIMPEL» special technological program was created. Main results of a study of radar errors with orbits of space surveillance catalogue was presented. Also, the results were compared with data of measuring instrument's calibration software complex. This software complex provides determination of satellite's position with errors less than 10 m. A new dynamic model of measuring instrument errors is proposed.

Spatio‐temporal‐dependent errors of radar rainfall estimates in flood forecasting for the Nam River Dam basin

ABSTRACTIn flood prediction, radar rainfall estimates have been widely used for calculating approximate rainfall amounts and predicting flood risks. However, radar rainfall estimates have a number of errors, such as beam blockage and ground clutter, that hinder their application in hydrological flood forecasting. Even though previous studies have focused on removing radar data error, it is important to evaluate runoff volume, which is primarily influenced by such radar errors. Furthermore, correlation structures including temporal as well as spatially dependent errors have not been thoroughly studied. Therefore, how those radar rainfall estimate errors influence flood forecasting was tested in this paper by using a spatio‐temporal error model (STEM), which is a cross‐correlation model of radar error. Rainfall‐runoff simulations were conducted with radar rainfall events generated using the STEM to investigate the response in a basin. The Nam River basin, South Korea, was the focus of the study. A distributed rainfall runoff model, Vflo™, was used for runoff simulation. The spatial and temporal resolutions were 0.5 km and 10 min, respectively. The results indicated that a strong correlation caused a higher variation in the peak discharge. It is concluded that the STEM effectively represents the radar rainfall profile. The spatio‐temporal error (STE) of the radar rainfall estimates caused much higher uncertainty in rainfall runoff than only spatial error. To reduce uncertainty in flood prediction using radar rainfall estimates, it is important to eliminate the STE from those estimates.

Regional frequency analysis of extreme rainfall in Belgium based on radar estimates

Abstract. In Belgium, only rain gauge time series have been used so far to study extreme rainfall at a given location. In this paper, the potential of a 12-year quantitative precipitation estimation (QPE) from a single weather radar is evaluated. For the period 2005–2016, 1 and 24 h rainfall extremes from automatic rain gauges and collocated radar estimates are compared. The peak intensities are fitted to the exponential distribution using regression in Q-Q plots with a threshold rank which minimises the mean squared error. A basic radar product used as reference exhibits unrealistic high extremes and is not suitable for extreme value analysis. For 24 h rainfall extremes, which occur partly in winter, the radar-based QPE needs a bias correction. A few missing events are caused by the wind drift associated with convective cells and strong radar signal attenuation. Differences between radar and gauge rainfall values are caused by spatial and temporal sampling, gauge underestimations and radar errors. Nonetheless the fit to the QPE data is within the confidence interval of the gauge fit, which remains large due to the short study period. A regional frequency analysis for 1 h duration is performed at the locations of four gauges with 1965–2008 records using the spatially independent QPE data in a circle of 20 km. The confidence interval of the radar fit, which is small due to the sample size, contains the gauge fit for the two closest stations from the radar. In Brussels, the radar extremes are significantly higher than the gauge rainfall extremes, but similar to those observed by an automatic gauge during the same period. The extreme statistics exhibit slight variations related to topography. The radar-based extreme value analysis can be extended to other durations.

Algorithm for Estimating the Parameters of Sea Pitching for Increasing the Accuracy of a Ship-Borne Radar Beam Positioning

The sea waves cause the effect of a rotational motion (i.e., pitch, roll and heading angle) of ships. The ship rotational motions result in beam pointing error of the phased array radar aboard the ship. The antenna stabilization aimed to achieve a beam pointing accuracy over a long dwell time is an important problem for the shipborne phased array radars. Due to the dynamic and stochastic nature of the sea environment, the shipborne phased array radar must be able to compensate for the ship's motion adaptively. In this paper, the linear discrete Kalman filter is proposed as a predictor for the shipborne phased array radar, which can compensate for the beam pointing error and track the air and sea surface targets. The pitch, roll and heading angles and the its velocities data are measured on-line from a gyroscope of the sea vehicle and used from the ship motion mathematical models for their prediction. It is proved, that the pitch, roll, and heading motion models may be considered as independent. All these models are presented as the same second order linear differential equations with different parameters. Besides, equivalent linear discrete state space models for the angles' changes are constructed in the paper. The estimation accuracy of the Kalman filter (predictor) depends on the values of different parameters, such as the parameters of the ship's motion mathematical model, measurement error covariance matrices, etc. The sea environments are very dynamic, hence, there is a need for an adaptive system for the controlling and compensating devices, operating regardless of the ship's motion. Continuous monitoring of the environment and adapting filter ensure parameters with less computational burden needed for a real time application. The paper describes a technique for identification of such parameters by the measured correlation functions of the pitch, roll, and heading angles. Finally, it is proved by the computer simulations that the proposed compensations technique is a real time applicable algorithm for a shipborne phased array radar. The computer simulation was performed with the following parameters: the measurement frequency for the gyroscopes was 100 Hz, the prediction times of the Kalman filter were 0.01 s and 0.1 s. The following two cases were considered. In the first case, only the predicted angles were measured with gyroscopes. In the second case, the angles and the rates of their change were measured. The simulations demonstrated that the presented prediction algorithm ensured higher accuracy (less root mean square errors of the predicted angles) than the initial accuracy of the gyroscopes measurements.

Representing radar rainfall uncertainty with ensembles based on a time-variant geostatistical error modelling approach

The application of radar quantitative precipitation estimation (QPE) to hydrology and water quality models can be preferred to interpolated rainfall point measurements because of the wide coverage that radars can provide, together with a good spatio-temporal resolutions. Nonetheless, it is often limited by the proneness of radar QPE to a multitude of errors. Although radar errors have been widely studied and techniques have been developed to correct most of them, residual errors are still intrinsic in radar QPE. An estimation of uncertainty of radar QPE and an assessment of uncertainty propagation in modelling applications is important to quantify the relative importance of the uncertainty associated to radar rainfall input in the overall modelling uncertainty. A suitable tool for this purpose is the generation of radar rainfall ensembles. An ensemble is the representation of the rainfall field and its uncertainty through a collection of possible alternative rainfall fields, produced according to the observed errors, their spatial characteristics, and their probability distribution. The errors are derived from a comparison between radar QPE and ground point measurements. The novelty of the proposed ensemble generator is that it is based on a geostatistical approach that assures a fast and robust generation of synthetic error fields, based on the time-variant characteristics of errors. The method is developed to meet the requirement of operational applications to large datasets. The method is applied to a case study in Northern England, using the UK Met Office NIMROD radar composites at 1km resolution and at 1h accumulation on an area of 180km by 180km.The errors are estimated using a network of 199 tipping bucket rain gauges from the Environment Agency. 183 of the rain gauges are used for the error modelling, while 16 are kept apart for validation. The validation is done by comparing the radar rainfall ensemble with the values recorded by the validation rain gauges. The validated ensemble is then tested on a hydrological case study, to show the advantage of probabilistic rainfall for uncertainty propagation. The ensemble spread only partially captures the mismatch between the modelled and the observed flow. The residual uncertainty can be attributed to other sources of uncertainty, in particular to model structural uncertainty, parameter identification uncertainty, uncertainty in other inputs, and uncertainty in the observed flow.